Simulation of Backpropagation Neural Networks

Backpropagation (BP) neural networks are classic feedforward neural networks commonly employed for solving classification and regression problems. Simulating BP neural networks in MATLAB allows for intuitive observation of the training process and performance metrics. The Levenberg-Marquardt (LM) algorithm is used for training, which effectively enhances convergence speed and enables the network to approach optimal solutions more rapidly.

The LM algorithm combines the advantages of gradient descent and Gauss-Newton methods by dynamically adjusting the damping factor to balance convergence speed and stability. During training, the downward trend of the error curve can be observed – a smooth curve that rapidly converges to low error values indicates effective network training. In MATLAB implementation, this can be monitored using functions like `trainlm` and plotting tools to visualize error progression.

To optimize training curves, parameters such as learning rate, number of hidden layer nodes, and training epochs can be adjusted, along with appropriate activation function selection (e.g., Sigmoid or ReLU). Code implementation typically involves setting these parameters in the `train` function configuration. Additionally, data preprocessing (e.g., normalization using `mapminmax`) and regularization techniques (like L2 regularization) can significantly improve the network's generalization capability, which can be implemented through MATLAB's neural network toolbox options.

After training completion, network performance can be validated using test datasets, and training error curves can be visualized to assess model convergence. MATLAB provides functions like `plotperform` and `confusionmat` for performance evaluation and result visualization, enabling comprehensive analysis of the trained network's accuracy and stability.